What is that big box?
 

I recently spent two weeks in an older home in Alhambra, probably built in the late 90s. I like to look at the mechanical systems and try to figure out how they work.
In the garage, the HVAC unit sat atop a large box-like structure. Probably 3' x 3'. I've seen the same set up in pictures of other homes. So, what is the purpose of this? Is it some sort of air return system for the Air Conditioner? Just a stand to support the air exchanger?

Yes, it's part of the air return system. The return air comes down into that box and then goes upward through the cooling coils and into the supply ductwork that distributes the cool air throughout the house. You may have been looking at a heat pump because that's the way mine looks.

I always thought the big “box” is there to support the air handler that sits on top of it. I don’t think any air is exchanged in that box structure. I may be wrong though. I will ask our HVAC company when they come to do the winter service.

Just had a new system installed. Asked installer about this.
He said it is just cosmetic except when a heat pump is involved… then it is part of the air handling system.

The large return air duct is located inside the box structure. It feeds air into the bottom of the air handler, which is cooled (or heated) by the evaporator coil and then blown upward to the ducts located in the attic. In hot climates, like Florida, the supply air registers are located in the ceiling. In cold climates, the supply air is more likely to be delivered through the floor.

If you are referring to the wooden box structure return line is only there when a heat pump is installed. Otherwise you are correct.
My new (non heat pump) system, as was the old one, all sits on top of a wooden box structure.

Yes, it is.

A picture would be helpful.

A picture would be helpful, you say?
 

Here's three, clipped from homes for sale . . .

Posts #2 and #5 look correct to me. The installation is slightly different in my home but when I remove the air filter I can see down into the empty space where the return air ducts tie in.

One thing check is how to remove/replace the air cleaner. In a couple of those pictures it looks like it could be difficult to maneuver the filter in and out of the unit.